Spectral Methods in Algebra, Geometry, and Topology

Explore advanced mathematical concepts through this comprehensive summer school lecture series covering spectral methods across algebra, geometry, and topology. Delve into tensor triangular geometry with Greg Stevenson's three-part exploration of this fundamental framework in algebraic topology. Master equivariant stable homotopy theory through Stefan Schwede's detailed lectures examining group actions on stable homotopy categories. Investigate spectral methods in finite group representation theory with Dave Benson's systematic treatment of how spectral techniques illuminate the structure of group representations. Gain foundational knowledge in chromatic homotopy theory through Agnes Beaudry's introductory lectures and Mike Hill's complementary presentation, covering the chromatic filtration and its applications to stable homotopy theory. Each topic is presented through multiple interconnected lectures that build understanding progressively, making advanced concepts in algebraic topology, representation theory, and homotopy theory accessible to graduate students and researchers seeking to understand how spectral methods unify diverse areas of mathematics.